Preheat the oven to 350°F. Line two baking sheets with parchment.
In a large bowl, combine the oats, flour, brown sugar, baking soda, and salt, whisking to blend. Add the butter, and use your fingers, pressing and squeezing, to work it into the oat mixture until it resembles a coarse meal. Stir in the yogurt until a soft dough forms. (If your yogurt is on the thick side, you may need to add a tablespoon or so of milk, just enough to bring the dough together.) The dough should be a little crumbly. Lightly flour a work surface, and turn the dough out onto it, rolling or patting it to a ¼-inch thickness. (I found that the dough was a little too sticky to roll cleanly, but it worked out alright.) Using a 2-inch round cookie cutter, stamp out oatcakes, and transfer them to the prepared sheet pans. (A bench scraper comes in handy for transferring the oatcakes to the sheet pans and cleaning the counter afterward. I found that I could comfortably fit about 15 oatcakes on one pan and the remainder on the second.) (I am really into parentheses today.) It’s okay to gather and re-roll any scraps of dough.
Bake the oatcakes for about 15 minutes, or until they are golden brown around the edges. Transfer to a wire rack to cool completely, and then store in an airtight container at room temperature.
Yield: about 25 oatcakes